Telecommunications systems, cable television systems and data communication networks may use optical networks to rapidly convey large amounts of information between remote points. In an optical network, information may be conveyed in the form of optical signals through optical fibers. Optical fibers may comprise thin strands of glass capable of communicating the signals over long distances with very low loss. Optical networks often employ modulation schemes to convey information in the optical signals over the optical fibers. Such modulation schemes may include phase-shift keying (“PSK”), frequency-shift keying (“FSK”), amplitude-shift keying (“ASK”), and quadrature amplitude modulation (“QAM”).
In PSK, the information carried by the optical signal may be conveyed by modulating the phase of a reference signal, also known as a carrier wave. The information may be conveyed by modulating the phase of the signal itself using differential phase-shift keying (“DPSK”).
In QAM, the information carried by the optical signal may be conveyed by modulating both the amplitude and phase of the carrier wave. PSK may be considered a subset of QAM, wherein the amplitude of the carrier waves are maintained as a constant.
PSK and QAM signals may be represented using a complex plane with real and imaginary axes on a constellation diagram. The points on the constellation diagram representing symbols carrying information may be positioned with uniform angular spacing around the origin of the diagram. The number of symbols to be modulated using PSK and QAM may be increased and thus increase the information that can be carried. The number of signals may be given in multiples of two. As additional symbols are added, they may be arranged in uniform fashion around the origin. PSK signals may include such an arrangement in a circle on the constellation diagram, meaning that PSK signals have constant powers for all symbols. QAM signals may have the same angular arrangement as that of PSK signals, but include different amplitude arrangement. QAM signals may have its symbols arranged around multiple circles, meaning that the QAM signals include different power for different symbols. This arrangement may decrease the risk of noise as the symbols are separated by as much distance as possible. A number of symbols “m” may thus be used and denoted “m-PSK” or “m-QAM.”
Examples of PSK and QAM with a different number of symbols can include binary PSK (“BPSK” or “2-PSK”) using two phases at 0° and 180° (or 0 and π) on the constellation diagram; quadrature PSK (“QPSK”, “4-PSK”, or “4-QAM”) using four phases at 0°, 90°, 180°, and 270° (or 0, π/2, π, and 3π/2); eight-phase PSK (“8-PSK”) and QAM (“8-QAM”) using eight phases at 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315° (or 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, and 7π/4); and sixteen-phase PSK (“16-PSK”) and QAM (“16-QAM”) using sixteen phases at 0°, 22.5°, 45°, 67.5°, 90°, 112.5°, 135°, 157.5°, 180°, 202.5°, 225°, 247.5°, 270°, 292.5°, 315°, and 337.5° (or 0, π/8, π/4, 3π/8, π/2, 5π/8, 3π/4, 7π/8, π, 9π/8, 5π/4, 11π/8, 3π/2, 13π/8, 7π/4, and 15π/8).
Phases in such signals may be offset. Each of 2-PSK, 4-PSK, 8-PSK and 16-PSK signals may be arranged in one circle on the constellation diagram. 8-QAM signals may be arranged in two circles and 16-QAM is arranged in three circles.
M-PSK and m-QAM signals may also be polarized using techniques such as dual-polarization QPSK (“DPQPSK”), wherein separate m-PSK signals are multiplexed by orthogonally polarizing the signals.